I understand that there is approx 1 hydrogen atom per cubic centimeter in interstellar space. Assuming they don’t get pulled into a star or planet millions of years from now, how long before these probes lose all their momentum from the slight friction with these atoms?
Interesting thought. According to my reference the mean column density of the interstellar gas is 1.8x10^17 atoms per cm^2 per parsec. That’s about 3x10^-7 grams per cm^2.
Now, friction would never completely stop the spacecraft, the speed will just decay exponentially. Let’s say the speed drops appreciably low after the spacecraft plows through its own weight in interstellar gas. Assuming the spacecraft is about 100 gram per cm^2 in column density, it will take 3x10^9 parsecs.
That means this calculation is meaningless, because other concerns come up long before that. Such as, does the spacecraft have enough kinetic energy so it can escape the gravitational well of the Galaxy? I suspect the answer is no. So the spacecraft will forever be part of the Galaxy, going around the Galaxy much the same way asteroids or comets do around the solar system.
Well (bearing in mind that IANAPhysicist), if the spacecraft are orbiting the galactic center, and they’re also encountering friction with the interstellar medium, I would think that would eventually cause their orbits to decay and they’d fall into the black hole at the center of the galaxy.
Whether or not this would happen before the heat death of the entire Universe I haven’t the math to calculate.
Given that we are in a spiral galaxy, I should think it safe to assume that the interstellar medium is rotating around the galactic centre along with everything else.